Q. 10 Riemann sums: Calculate each of ... [FREE SOLUTION]

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Chapter 4: Q. 10 (page 404)

Riemann sums: Calculate each of the following Riemann sum
approximations for the definite integral of f on [a, b], using the
given value of n.
The trapezoid sum for $f (x) = 9 - x^{2}$ on $[0, 3], n = 6$

Short Answer

Expert verified

The trapezoid sum is $17 路 8$ .

Step by step solution

Step 1. Given information .

Consider the given function $f (x) = 9 - x^{2}$ .

Step 2. Formula used .

${鈭�}_{a}^{b} f (x) d x = \frac{未 x}{2} [f (x_{0}) + f (x_{n}) + 2 [f (x_{i}) + f (x_{2}) + . . . . . . . . . . . . . + f (x_{n - 1})]]$

Step 3. Find the trapezoid sum .

Trapezoid sum for $f (x) = 9 - x^{2}$ on $[0, 3], n = 6$ .

$未 x = \frac{3 - 0}{6} = 0 路 5$

$x$	$0$	$0 路 5$	$1$	$1 路 5$	$2$	$2 路 5$	$3$
$f (x)$	$9$	$8 路 75$	$8$	$6 路 75$	$5$	$2 路 75$	$0$

$= 2 [f (x_{1}) + f (x_{2}) + . . . . . . . . . . . . . + f (x_{n - 1})] = 2 [8 路 75 + 8 + 6 路 75 + 5 + 2 路 75] = 62 路 50 {鈭�}_{0}^{3} f (x) d x = \frac{1}{4} [9 + 0 + 62 路 5] = 17 路 8$

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91影视

Riemann sums: Calculate each of the following Riemann sum
approximations for the definite integral of f on [a, b], using the
given value of n.
The trapezoid sum for $f (x) = 9 - x^{2}$ on $[0, 3], n = 6$

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Formula used .

Step 3. Find the trapezoid sum .

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91影视

Riemann sums: Calculate each of the following Riemann sumapproximations for the definite integral of f on [a, b], using thegiven value of n.The trapezoid sum forfx=9-x2on0,3,n=6

Short Answer

Step by step solution

Step 1. Given information .

Step 2. Formula used .

Step 3. Find the trapezoid sum .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Calculus

Statistics

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

Riemann sums: Calculate each of the following Riemann sum
approximations for the definite integral of f on [a, b], using the
given value of n.
The trapezoid sum for $f (x) = 9 - x^{2}$ on $[0, 3], n = 6$